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In this work, we consider a Shallow‐Water Quasi Geostrophic equation on the sphere, as a model for global large‐scale atmospheric dynamics. This equation, previously studied by Verkley (2009, https://doi.org/10.1175/2008jas2837.1) and Schubert et al. (2009, https://doi.org/10.3894/james.2009.1.2), possesses a rich geometric structure, called Lie‐Poisson, and admits an infinite number of conserved quantities, called Casimirs. In this paper, we develop a Casimir preserving numerical method for long‐time simulations of this equation. The method develops in two steps: first, we construct an N‐dimensional Lie‐Poisson system that converges to the continuous one in the limit N → ∞; second, we integrate in time the finite‐dimensional system using an isospectral time integrator, developed by Modin and Viviani (2020, https://doi.org/10.1017/jfm.2019.944). We demonstrate the efficacy of this computational method by simulating a flow on the entire sphere for different values of the Lamb parameter. We particularly focus on rotation‐induced effects, such as the formation of jets. In agreement with shallow water models of the atmosphere, we observe the formation of robust latitudinal jets and a decrease in the zonal wind amplitude with latitude. Furthermore, spectra of the kinetic energy are computed as a point of reference for future studies. Plain Language Summary We conducted a study on a model that represents the movements of planetary flows. This model has important physical and mathematical properties that are related to its long‐term behavior, which is essential for understanding geophysical turbulence. In this work, we developed a numerical method for simulation that preserves the key mathematical structure of the model through a two‐step process. We applied our method to simulate global atmospheric flow and investigate the impact of varying strengths of planetary rotation. Our findings demonstrate the expected formation of wind patterns known as zonal jets, where stronger winds occur near the equator and weaker winds near the poles. We also present energy spectra that illustrate the influence of planetary rotation on the transfer of turbulent energy, which aligns with existing theoretical predictions found in literature. These results highlight the potential of our numerical method for studying fundamental problems in geophysical fluid dynamics. Key Points We develop a numerical method preserving Casimirs to simulate balanced shallow water flow on the sphere We perform global high‐resolution simulations while accurately accounting for latitude‐dependent effects Our simulations show the formation of robust zonal jets and provide key insights into quasi‐geostrophic turbulence

We propose a point-particle model for two-way coupling of water droplets dispersed in the turbulent flow of a carrier gas consisting of air and water vapour. We adopt an Euler–Lagrangian formulation based on conservation laws for the mass, momentum and energy of the continuous phase and on empirical correlations describing momentum, heat and mass transfer between the droplet phase and the carrier gas phase. An incompressible flow formulation is applied for direct numerical simulation of differentially heated turbulent channel flow. The two-way coupling is investigated in terms of its effects on mass and heat transfer characteristics and the resulting droplet size distribution. Compared to simulations without droplets or those with solid particles with the same size and specific heat as the water droplets, a significant increase in Nusselt number is found, arising from the additional phase changes. The Nusselt number increases with increasing ambient temperature and is almost independent of the heat flux applied to the walls of the channel. The time-averaged droplet size distribution displays a characteristic dependence on position expressing the combined effect of turbophoresis and phase changes in turbulent wall-bounded flow. In the statistically steady state that is reached after a long time, the resulting flow exhibits a mean motion of water vapour from the warm wall to the cold wall, where it condenses on average, followed by a net mean mass transfer of droplets from the cold wall to the warm wall.

We present Direct Numerical Simulation of biomass pyrolysis and combustion in a turbulent channel flow. The model includes simplified models for biomass pyrolysis and char combustion along with a model for particle tracking. The gas phase is modelled as a mixture of reacting gas species. The gas-particle interactions for mass, momentum, and energy exchange are included by two-way coupling terms. The effect of two-way coupling on the conversion time of biomass particles is found noticeable for particle volume fractions > 10-5. We also observe that at constant volume fraction the effect of two-way coupling increases as the particle size is reduced, due to the higher total heat exchange area in case of smaller particles. The inclusion of gas phase homogeneous reactions in the DNS model decreases the biomass pyrolysis time due to higher gas temperatures. In contrast, including gas phase reactions increases the combustion time of biomass due to the lower concentration of oxygen at the particle surface.

A mathematical model describing fluid flow and concentration dynamics of microorganisms inside a UV photoreactor is developed. Using physical arguments and techniques from system theory, we approximate this model by a first-order linear one. For this reduced model, we design a controller. The controller is tested on the original model as well as on the reduced model by numerical simulation. This showed only small differences in dynamics, which indicates that for the original model a classic controller with excellent properties can be designed.

This chapter examines dynamic self-organization in particle-laden turbulent channel flow. Many flows of relevance to large-scale chemical processing involve solid catalyst particles at significant concentrations embedded in a carrying gas-flow. Control over the spatial distribution of these particles, especially its homogeneity, is essential in order to provide a chemical processing that is as complete and uniform as possible, that is consistent with modern environmental requirements and that does not constitute a strong safety hazard. This chapter analyzes the fundamental aspects turbulent riser-flow which contains large numbers of interacting particles. Particle-particle as well as particle-fluid interactions are also included in the chapter. These interactions and the flow-forcing are the source for the dynamic formation and destruction of large-scale coherent particle swarms in the flow. The basic scenario of this self-organization is established, and the dominant aspects of the resulting turbulence modulation are investigated. Large-eddy simulations with different subgrid models and large numbers of particles at a significant volume fraction and realistic mass load ratio indicate the development of a thinner boundary layer and an accumulation of particles near the walls. At an average volume fraction of ≈ 1.5% it is found that neglecting particle-particle interactions leads to an unphysical modulated flow.

Roland Kuiper and colleagues identify a homozygous germline nonsense mutation in the base-excision repair gene NTHL1 in three families with recessive inheritance of adenomatous polyposis. The genetic cause underlying the development of multiple colonic adenomas, the premalignant precursors of colorectal cancer (CRC), frequently remains unresolved in patients with adenomatous polyposis. Here we applied whole-exome sequencing to 51 individuals with multiple colonic adenomas from 48 families. In seven affected individuals from three unrelated families, we identified a homozygous germline nonsense mutation in the base-excision repair (BER) gene NTHL1 . This mutation was exclusively found in a heterozygous state in controls (minor allele frequency of 0.0036; n = 2,329). All three families showed recessive inheritance of the adenomatous polyposis phenotype and progression to CRC in at least one member. All three affected women developed an endometrial malignancy or premalignancy. Genetic analysis of three carcinomas and five adenomas from different affected individuals showed a non-hypermutated profile enriched for cytosine-to-thymine transitions. We conclude that a homozygous loss-of-function germline mutation in the NTHL1 gene predisposes to a new subtype of BER-associated adenomatous polyposis and CRC.

On the basis of maps of environmental variables and annual surveys, a habitat map was constructed for the cockle Cerastoderma edule, a commercially exploited dominant suspension feeder in the Eastern Scheldt (The Netherlands). The results obtained show that the distribution of cockles can be described using emersion time and current velocity. Salinity does not play a significant role, even though low salinities are known to limit the distribution of cockles in other areas. The response to current velocity was as expected, but the response to emersion contradicted results from other studies. These responses cannot be explained as the result of competition for space with the recently expanded Pacific oyster population, because Pacific oysters are most common in habitats that are unsuitable for cockles. Possible explanations for cockles' apparent preference for settling in areas with relatively long emersion times are high predation pressure or instability of the sediment around low water level.